Abstract
The optimization of a magnetohydrodynamic flow of Al2O3–water nanofluid was carried out numerically considering the combined effects of various parameters such as porous medium permeability, Forchheimer drag, slip length, conduction–radiation parameter and nanoparticle volume fraction on heat transfer and entropy generation. The numerical computations were made by using the shooting technique together with Runge–Kutta–Fehlberg method, and the results were compared with already published studies obtaining a very good agreement. Here, optimal operating conditions with minimum entropy and maximum or minimum heat transfer not yet reported in previous similar configurations were reached and the effects of porous medium in the presence of combined convective–radiative boundary conditions and nonlinear radiation heat flux were analyzed. Results showed that the global entropy increased with the porous medium permeability, while it decreased with the inertia parameter. In addition, optimum values of slip length and nanoparticle volume fraction that minimize the global entropy, were found. These optimum values of both quantities moved to higher values as the porous medium permeability increased. The Nusselt number was also explored for different conditions. Optimum values of Grashof number and conduction–radiation parameter with maximum heat transfer, as well as slip length with minimum heat transfer were found. These optimum values of Grashof moved to lower values as the permeability increased, while their optimum values shifted toward higher values with the inertia parameter. The obtained optimum values of slip length with minimum heat transfer moved to higher values when the permeability increased. Finally, four different models were defined to show the effects of uncertainties in thermophysical properties of nanofluid on heat transfer and entropy generation. These models were obtained from the combination of two relations used for both the dynamic viscosity and the thermal conductivity of nanofluid. It was seen that, independent of the model, optimal operating conditions were achieved for the explored values.
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References
Mahdi RA, Mohammed HA, Munisamy KM, Saeid NH. Review of convection heat transfer and fluid flow in porous media with nanofluid. Renew Sustain Energy Rev. 2015;41:715–34.
Ibáñez G, López A, Pantoja J, Moreira J. Combined effects of uniform heat flux boundary conditions and hydrodynamic slip on entropy generation in a microchannel. Int J Heat Mass Transf. 2014;73:201–6.
Hooman K. Heat transfer and entropy generation for forced convection through a microduct of rectangular cross-section: effects of velocity slip, temperature jump, and duct geometry. Int Commun Heat Mass Transf. 2008;35(9):1065–8.
Yazdi MH, Abdullah S, Hashim I, Sopian K, Zaharim A. Entropy generation analysis of liquid fluid past embedded open parallel microchannels within the surface. Eur J Sci Res. 2009;28(3):462–70.
Ibáñez G, López A, Pantoja J, Moreira J, Reyes JA. Optimum slip flow based on the minimization of entropy generation in parallel plate microchannels. Energy. 2013;50:143–9.
Rashidi MM, Kavyani N, Abelman S. Investigation of entropy generation in MHD and slip flow over a rotating porous disk with variable properties. Int J Heat Mass Transf. 2014;70:892–917.
Makinde OD. Second law analysis for variable viscosity hydromagnetic boundary layer flow with thermal radiation and Newtonian heating. Entropy. 2011;13:1446–64.
Torabi M, Aziz A. Entropy generation in a hollow cylinder with temperature dependent thermal conductivity and internal heat generation with convectiveradiative surface cooling. Int Commun Heat Mass Transf. 2012;39(10):1487–95.
Torabi M, Zhang K. Classical entropy generation analysis in cooled homogenous and functionally graded material slabs with variation of internal heat generation with temperature, and convectiveradiative boundary conditions. Energy. 2014;65:387–97.
Ibáñez G. Entropy generation in MHD porous channel with hydrodynamic slip and convective boundary conditions. Int J Heat Mass Transf. 2015;80:274–80.
Vyas P, Soni S. Entropy analysis for MHD Casson fluid flow in a channel subjected to weakly temperature dependent convection coefficient and hydrodynamic slip. J Rajasthan Acad Phys Sci. 2016;15(1):1–18.
Vyas P, Srivastava N. Entropy analysis of generalized MHD Couette flow inside a composite duct with asymmetric convective cooling. Arab J Sci Eng. 2015;40(2):603–14.
Ibáñez G, Cuevas S. Entropy generation minimization of a MHD (magnetohydrodynamic) flow in a microchannel. Energy. 2010;35:4149–55.
Mondal PK, Mukherjee S. Viscous dissipation effects on the limiting value of Nusselt numbers for a shear driven flow between two asymmetrically heated parallel plates. Front Heat Mass Transf. 2012;3:1–6.
Mondal PK. An analytical approach to the effect of viscous dissipation on shear-driven flow between two parallel plates with constant heat flux boundary conditions. Int J Eng. 2013;26(5):533–42.
Ibáñez GA, López A, Cuevas S. Optimum wall thickness ratio based on the minimization of entropy generation in a viscous flow between parallel plates. Int Commun Heat Mass Transf. 2012;39:587–92.
Mondal PK, Dholey S. Effect of conjugate heat transfer on the irreversibility generation rate in a combined Couette–Poiseuille flow between asymmetrically heated parallel plates: the entropy minimization analysis. Energy. 2015;83:5564.
Meibodi SS, Kianifar A, Mahian O, Wongwises S. Second law analysis of a nanofluid-based solar collector using experimental data. J Therm Anal Calorim. 2016;126:61725.
Mahian O, Mahmud S, Heris SZ. Analysis of entropy generation between co-rotating cylinders using nanofluids. Energy. 2012;44:438–46.
Torabi M, Zhang K, Mahmud S. Temperature and entropy generation analyses between and inside rotating cylinders using copper-water nanofluid. J Heat Transf. 2015;137:051701.
Sheikholeslami M, Ganji DD. Magnetohydrodynamic flow in a permeable channel filled with nanofluid. Sci Iran. 2014;21:203–12.
Sheikholeslami M, Gorji-Bandpy M, Ganji DD. Lattice Boltzmann method for MHD natural convection heat transfer using nanofluid. Powder Technol. 2014;254:82–93.
Mahian O, Kianifar A, Kleinstreuer C, Al-Nimr MA, Pop I, Sahin AZ. A review of entropy generation in nanofluid flow. Int J Heat Mass Transf. 2013;65:514–32.
Mahian O, Mahmud S, Wongwises S. Entropy generation between two rotating cylinders with magnetohydrodynamic flow using nanofluids. J Thermophys Heat Transf. 2013;27(1):161–9.
Rashidi MM, Abelman S, Mehr NF. Entropy generation in steady MHD flow due to a rotating porous disk in a nanofluid. Int J Heat Mass Transf. 2013;62:515–25.
Habibi MM, Hosseini R, Simiari M, Jahangiri P. Entropy generation minimization of nanofluid flow in a MHD channel considering thermal radiation effect. Mechanics. 2013;19(4):445–50.
Hayat T, Nawaz S, Alsaedi A, Rafiq M. Analysis of entropy generation in mixed convective peristaltic flow of nanofluid. Entropy. 2016;18:355–73.
Hayat T, Rafiq M, Ahmad B, Asghar S. Entropy generation analysis for peristaltic flow of nanoparticles in a rotating frame. Int J Heat Mass Transf. 2017;108:1775–86.
Tlili I, Hamadneh NN, Khan WA, Atawneh S. Thermodynamic analysis of MHD Couette–Poiseuille flow of water-based nanofluids in a rotating channel with radiation and Hall effects. J Therm Anal Calorim. 2018;132(3):1899–912.
Sekrani G, Poncet S, Proulx P. Conjugated heat transfer and entropy generation of Al\(_2\)O\(_3\) water nanofluid flows over a heated wall-mounted obstacle. J Therm Anal Calorim. 2018;19:313. https://doi.org/10.1007/s10973-018-7349-x.
Shahriari A, Ashorynejad HR, Pop I. Entropy generation of MHD nanofluid inside an inclined wavy cavity by lattice Boltzmann method. J Therm Anal Calorim. 2018;1:1. https://doi.org/10.1007/s10973-018-7061-x.
Sheikholeslami M, Ellahi R, Ashorynejad HR, Domairry G, Hayat T. Effects of heat transfer in flow of nanofluids over a permeable stretching wall in a porous medium. J Comput Theor Nanosci. 2014;11:486–96.
Ting TW, Hung YM, Guo N. Entropy generation of viscous dissipative nanofluid flow in thermal non-equilibrium porous media embedded in microchannels. Int J Heat Mass Transf. 2015;81:862–77.
Baytas AC. Entropy generation for thermal nonequilibrium natural convection with a non-Darcy flow model in a porous enclosure filled with a heat-generating solid phase. J Porous Media. 2017;10:261–75.
Ismael MA, Armaghani T, Chamkha AJ. Conjugate heat transfer and entropy generation in a cavity filled with a nanofluid-saturated porous media and heated by a triangular solid. J Taiwan Inst Chem Eng. 2016;59:138–51.
Torabi M, Torabi M, Ghiaasiaan SM, Peterson GP. The effect of Al\(_2\)O\(_3\)-water nanofluid on the heat transfer and entropy generation of laminar forced convection through isotropic porous media. Int J Heat Mass Transf. 2017;111:804–16.
Shit GC, Haldar R, Mandal S. Entropy generation on MHD flow and convective heat transfer in a porous medium of exponentially stretching surface saturated by nanofluids. Adv Powder Technol. 2017;28(6):1519–30.
Malik S, Nayak AK. MHD convection and entropy generation of nanofluid in a porous enclosure with sinusoidal heating. Int J Heat Mass Transf. 2017;111:329–45.
Al-Zamily A. Analysis of natural convection and entropy generation in a cavity filled with multi-layers of porous medium and nanofluid with a heat generation. Int J Heat Mass Transf. 2017;106:1218–31.
Chamkha AJ, Rashad AM, Armaghani T, et al. Effects of partial slip on entropy generation and MHD combined convection in a lid-driven porous enclosure saturated with a Cu-water nanofluid. J Therm Anal Calorim. 2018;132(2):1291–306.
Ghasemi K, Siavashi M. Lattice Boltzmann numerical simulation and entropy generation analysis of natural convection of nanofluid in a porous cavity with different linear temperature distributions on side walls. J Mol Liq. 2017;233:415–30.
Mohseni-Gharyehsafa B, Ebrahimi-Moghadam A, Okati V. Optimizing flow properties of the different nanofluids inside a circular tube by using entropy generation minimization approach. J Therm Anal Calorim. 2018;12:158. https://doi.org/10.1007/s10973-018-7276-x.
Alizadeh R, Karimi N, Arjmandzadeh R, Mehdizadeh A. Mixed convection and thermodynamic irreversibilities in MHD nanofluid stagnation-point flows over a cylinder embedded in porous media. J Therm Anal Calorim. 2018;119:2195. https://doi.org/10.1007/s10973-018-7071-8.
Bejan A. Entropy generation through heat and fluid flow. New York: Wiley; 1982.
López A, Ibáñez G, Pantoja J, Moreira J, Lastres O. Entropy generation analysis of MHD nanofluid flow in a porous vertical microchannel with nonlinear thermal radiation, slip flow and convective-radiative boundary conditions. Int J Heat Mass Transf. 2017;107:982–94.
Ibáñez G, López A, Pantoja J, Moreira J. Entropy generation analysis of a nanofluid flow in MHD porous microchannel with hydrodynamic slip and thermal radiation. Int J Heat Mass Transf. 2016;100:89–97.
Das S, Banu AS, Jana RN, Makinde OD. Entropy analysis on MHD pseudo-plastic nanofluid flow through a vertical porous channel with convective heating. Alex Eng J. 2015;54(3):325–37.
Mahian O, Mahmud S, Heris SZ. Effect of uncertainties in physical properties on entropy generation between two rotating cylinders with nanofluids. J Heat Transf. 2012;134:101704–15.
Mahian O, Kianifar A, Sahin AZ, Wongwises S. Entropy generation during Al\({_2}\)O\({_3}\)/water nanofluid flow in a solar collector: effects of tube roughness, nanoparticle size, and different thermophysical models. Int J Heat Mass Transf. 2014;78:64–75.
Mansour RB, Galanis N, Nguyen CT. Effect of uncertainties in physical properties on forced convection heat transfer with nanofluids. Appl Therm Eng. 2007;27:240–9.
Xu HJ. Performance evaluation of multi-layered porous-medium micro heat exchangers with effects of slip condition and thermal non-equilibrium. Appl Therm Eng. 2017;116:516–27.
Hunta G, Karimi N, Torabi M. Analytical investigation of heat transfer and classical entropy generation in microreactors the influences of exothermicity and asymmetry. Appl Therm Eng. 2017;119:403–24.
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Ibáñez, G., López, A., López, I. et al. Optimization of MHD nanofluid flow in a vertical microchannel with a porous medium, nonlinear radiation heat flux, slip flow and convective–radiative boundary conditions. J Therm Anal Calorim 135, 3401–3420 (2019). https://doi.org/10.1007/s10973-018-7558-3
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DOI: https://doi.org/10.1007/s10973-018-7558-3